Block #298,704

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/7/2013, 12:06:04 PM · Difficulty 9.9920 · 6,511,184 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

902f54187d8868097f880650ed6e84f0c92a107a5ced2f47da33ce7105bbd0a6

View on Chainz ↗

Height

#298,704

Difficulty

9.991996

Transactions

Size

890 B

Version

Bits

09fdf372

Nonce

16,777

Timestamp

12/7/2013, 12:06:04 PM

Confirmations

6,511,184

Mined by

⛏️ P2SHAZptEvQsEVX9iEwknWo2hxb5nvvC1vm8wf

Merkle Root

87cf47eeb6b1a6ec661bbfd5f4b8666e22000d499471eef367552a015d671a6c

Transactions (2)

Coinbased8b2fde9f5c9aa…00aa228d260984

1 in → 1 out10.0100 XPM109 B

AZptEvQs…vC1vm8wf

f0549978db0261…f9ebfbf3ee9dab

3 in → 10 out29.9900 XPM690 B

AcX65PZQ…PWYRNejc AMJDChGB…VXxUjXFK AGLT6Xxz…HJdBMtPa Aadjczru…WXPUazmh AYpANtX5…cpBRh2BL

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.565 × 10⁹⁷(98-digit number)

25653439992060052435…25155206401049081839

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.565 × 10⁹⁷(98-digit number)

25653439992060052435…25155206401049081839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.565 × 10⁹⁷(98-digit number)

25653439992060052435…25155206401049081841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.130 × 10⁹⁷(98-digit number)

51306879984120104870…50310412802098163679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.130 × 10⁹⁷(98-digit number)

51306879984120104870…50310412802098163681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.026 × 10⁹⁸(99-digit number)

10261375996824020974…00620825604196327359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.026 × 10⁹⁸(99-digit number)

10261375996824020974…00620825604196327361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.052 × 10⁹⁸(99-digit number)

20522751993648041948…01241651208392654719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.052 × 10⁹⁸(99-digit number)

20522751993648041948…01241651208392654721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.104 × 10⁹⁸(99-digit number)

41045503987296083896…02483302416785309439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.104 × 10⁹⁸(99-digit number)

41045503987296083896…02483302416785309441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.209 × 10⁹⁸(99-digit number)

82091007974592167792…04966604833570618879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #298,704

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